Convolution of χ-orbital measures on complex Grassmannians

Let { SU(p+q)/S(U(p)× U(q))} be the Grassmannian of complex p-dimensional subspaces of Cp+q, where p and q are integers such that p≥ q ≥ 2. The aim of this paper is to extend the main result in~{anchouche2},~{Alhashami} to the case of convolution of χ-orbital measures where χ is a character of S(U(p)× U(q)). More precisely, we give sufficient conditions for the ν-smoothness of the Radon Nikodym derivative f_ a₁,...,aᵣ, χ=d(μa₁, χ*...*μaᵣ, χ) /dμ_SU(p+q) of the convolution μa₁, χ*...*μaᵣ, χ with respect to the Haar measure μSU(p+q) of $SU(p+q)$, where μaⱼ, χ are some orbital measures defined below.